Greatest Common Factor of 192 and 196

Created By : Jatin Gogia

Reviewed By : Rajasekhar Valipishetty

Last Updated : Apr 06, 2023

Make use of GCF Calculator to quickly find the Greatest Common Factor of numbers 192, 196 i.e. 4 largest integer by which both the numbers can be divided.

Greatest common factor (GCF) of 192 and 196 is 4.

GCF(192,196) = 4

GCF of 192 and 196

Greatest common factor or Greatest common divisor (GCD) can be calculated in following way;

GCF of:
and

Greatest Common Factor of 192 and 196

GCF of 192 and 196 is 4

Prime Factorization of 192


2 192
2 96
2 48
2 24
2 12
2 6
3 3
1

Prime factors of 192 are 2,3. Prime factorization of 192 in exponential form is:

192 = 26×31

Prime Factorization of 196


2 196
2 98
7 49
7 7
1

Prime factors of 196 are 2,7. Prime factorization of 196 in exponential form is:

196 = 22×72

∴ So by taking common prime factors GCF of 192 and 196 is 4

Greatest Common Factor of 192 and 196 by matching factors method

Factors of 192

List of positive integer factors of 192 that divides 192 without a remainder.

1,2,3,4,6,8,12,16,24,32,48,64,96,192

Factors of 196

List of positive integer factors of 196 that divides 196 without a remainder.

1,2,4,7,14,28,49,98,196

Greatest Common Factor

We found the factors and prime factorization of 192 and 196. The biggest common factor number is the GCF number.
So the greatest common factor 192 and 196 is 4.

Also check out the Least Common Multiple of 192 and 196

Properties of GCF 192 and 196

(i) The GCF of 192 and 196 is associative

GCF of 192 and 196 = GCF of 196 and 192

Related Greatest Common Factor of 192

Related Greatest Common Factor of 196

Frequently Asked Questions on GCF of 192 and 196

1. What is the GCF of 192 and 196?

Answer: GCF of 192 and 196 is 4.

2. What are the Factors of 192?

Answer: Factors of 192 are 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 64, 96, 192. There are 14 integers that are factors of 192. The greatest factor of 192 is 192.

3. What are the Factors of 196?

Answer: Factors of 196 are 1, 2, 4, 7, 14, 28, 49, 98, 196. There are 9 integers that are factors of 196. The greatest factor of 196 is 196.

4. How to Find the GCF of 192 and 196?

Answer:

Greatest Common Factor of 192 and 196 = 4

Step 1: Find the prime factorization of 192

192 = 2 x 2 x 2 x 2 x 2 x 2 x 3

Step 2: Find the prime factorization of 196

196 = 2 x 2 x 7 x 7

Step 3: Multiply those factors both numbers have in common in steps i) or ii) above to find the gcf:

GCF = 2 x 2 = 4

Step 4: Therefore, the greatest common factor of 192 and 196 is 4